reserve k,m,n for Element of NAT,
  a,X,Y for set,
  D,D1,D2 for non empty set;
reserve p,q for FinSequence of NAT;
reserve x,y,z,t for Variable;
reserve F,F1,G,G1,H,H1 for ZF-formula;

theorem Th18:
  H is being_equality implies H.1 = 0
proof
  assume H is being_equality;
  then consider x,y such that
A1: H = x '=' y;
  H = <* 0,x,y *> by A1,FINSEQ_1:def 10;
  hence thesis;
end;
